PHGN341: Thermal Physics Quiz 8 April 19, 2013 NAME:

PHGN341: Thermal Physics
Quiz 8
April 19, 2013
As you know, the nucleus is composed of neutrons and protons which are spin-1/2 fermions. Let N equal the number of
neutrons, Z equal the number of protons, and A be the sum, A = N +Z. Nucleons bind together with short range forces which
means they pack together like hard spheres; so the nucleon density is approximately constant with the volume proportional
to A. The nuclear radius then scales like the cube root of the volume, R = r0 A 3 . A global fit to nuclear data gives r0 ' 1.2
fm which is constant for all nuclei. In this problem treat the nucleus as two degenerate Fermi gases, one of protons and one
of neutrons. (Data: h̄c = 197.3 MeV-fm, mp ' mn = 939 MeV/c2 , Lead (Pb): A = 208, Z = 82, and N = 126)
(a) Find the proton density for lead (i.e. number of protons per cubic femtometer, f m−3 ).
(b) What is the Fermi momentum (in MeV/c) of the protons in lead?
(c) What is the Fermi energy (in MeV) of the protons in lead?
(c) Examine the Z-dependence of your result from part (d) and re-scale your proton result to find the Fermi energy of the
neutrons in lead without re-doing the calculation.